The 23-year-old ironically came on as a second half substitute against Leicester in last Saturday's Heineken Cup quarter-final loss, and signed for the Zurich Premiership giants on Tuesday.
With the Tigers' long-time openside flanker Neil Back retiring at the end of the season to assume a coaching role, Jennings could prove to be a pivotal figure in new coach Pat Howard's first year in charge.
"We've done a lot of homework on Shane, as an individual and in the Leinster team," admitted Pat Howard, who takes over from current incumbent John Wells next month.
"He's a different sort of player to Neil Back - he can break defensive lines and he's only 23 years-old. It's important to have depth in our squad and the back row is one position where international call-ups and injuries can play a major role."
Jennings - who has captained Leinster in the Celtic League and scored an impressive four tries in seven European appearances this season - said: "I was delighted when my agent (John Baker) told me there was a chance that Leicester would be interested in me.
Jennings' move comes in a week when Connacht prop Peter Bracken and Munster scrum-half Eoin Reddan have also made the leap across the Irish sea.
Tighthead Bracken will link up with his former Galwegians coach John Kingston next season at NEC Harlequins, while 24-year-old Reddan has signed a two-year contract with 2004 Heineken Cup champions London Wasps.
Wasps head coach Shaun Edwards confirmed: "We've watched Eoin for a long time now and think he has all the attributes that we looking for in a number 9. His distribution and ball skills are good and we are looking forward to him playing for us next season."
Former Ireland Schools and Under-21 pivot Reddan will have fellow scrum-halves Harvey Biljon, Peter Richards, Warren Fury and England international Matt Dawson - who turns 33 in October - to compete with at the Causeway Stadium.